The Ingenious and Surprisingly Intuitive Prime Number Theorem

There are infinitely many prime numbers. So how can we determine how many prime numbers there are up to any value with no counting needed. Here’s the Prime Number Theorem explained in a very intuitive way.

Video Summary

If you started with the number one in the middle of some graphing paper and then charted all the other numbers around it in a spiral, you’d notice that, more and more, you’re running out of prime numbers. This makes perfect sense, of course. The higher you count, the more there are going to be composite numbers because there exists more options for factors. Still, the interesting thing about the spiral you’d be creating is that it actually shows up quite commonly in nature too. Known as the Design of Least Resistance, it’s the shape of galaxies, hurricanes, some seashells and even processes within our own bodies. As the spiral gets bigger, it continues moving away from the center, never to move any closer. The ratio of the length of that spiral and its distance from the center is roughly proportionate to the prime number spiral we spoke about at the beginning! Thanks to the Design of Least Resistance, we have the prime number theorem, which allows you to know roughly how many prime numbers exist below any given number.